Question

Monochromatic red light is incident on a double slit and produces an interference pattern on a screen some distance away. Explain how the fringe pattern would change if the red light source is replaced with a blue light source.

Answer 1

Since the interference pattern is a result of the wave portion of the wave-particle duality theorem of light, we can assume that by shifting the wavelength of the light from red to blue (or from long wavelength red light to short wavelength blue light) that the distance between areas of constructive interference (the brighter areas, or more "scientifically" known as fringes) would shift accordingly.


To determine the relationship between wavelength and the distance between the fringes, we need to study the behavior of the waves after passing through the slit. You can read more about the geometric and physical considerations by googling the Huygens–Fresnel principle.

However, if we understand the waves take on a cylindrical geometry after passing through the slit, we observe that the waves propagating from each slit interfere with each other. This interference creates for the brightly lit areas, aka fringes, through constructive interference, where the waves are in-phase and combine amplitudes; and creates for the areas of zero light through destructive interference, where the waves are out-of-phase and cancel amplitudes. We know from studying interference of waves that if two waves begin at the same point, they will constructively interfere at distances from the starting point equal to the wavelength, and destructively interfere at distances from the starting point equal to one-half the wavelength. Therefore, when we reduce the wavelength from red to blue, the distance from the starting point at which constructive interference occurs - and consequently destructive interference, will also decrease. Intuitively, we can conclude that there is a direct relationship between wavelength and the fringe pattern. Longer wavelengths create for fringes further apart, while shorter wavelengths create for fringes closer together.

Answer 2

Thank you so much for your explanation. Very clear and detailed.